dhruveshpotekar / steady-and-transient-state-simulation

Comparing fastest steady state simulation and fastest transient simulation for 2d conduction problem

Comparing-speed-of-Steady-Vs-Transient-State-simulation

We have to compare the fastest simulation of both the steady- and unsteady-state. The general 2 Dimensional heat conduction equation is frac{delT}{delt}=alpha(frac{del^2T}{delx^2} + frac{del^2T}{dely^2})

We will solve for two cases-
1.Transient / Unsteady state equation - Temperature within the system will change with time : frac{delT}{delt}=alpha(frac{del^2T}{delx^2} + frac{del^2T}{dely^2})

2.Steady state equation - Temperature within the system will not change with time : frac{del^2T}{delx^2} + frac{del^2T}{dely^2}=0

We assumed a plane wall of 10x10 matrix and specified the temperature values at all the sides of the wall as boundary conditions and calculated the temperature distribution at inner nodes.
The Boundary conditions for the problem are as follows;
Top Boundary = 600 K
Bottom Boundary = 900 K
Left Boundary = 400 K
Right Boundary = 800 K

For Steady-State

By Jacobi

By Gauss seidel

By Successive over relaxation

Comparing the three iterative solvers

From the above bar graph of steady-state heat conduction, the fastest simulation/lower number of iterations is achieved using successive over relaxation(SOR) iterative solver which used 94 iterations

For Unsteady-State

By Explicit method

By Implicit method

By Jacobi

By Gauss seidel

By Successive over relaxation

Comparing explicit and implicit unsteady-states

From above two bar graphs of transient state, we can see that the fastest simulation/low number of iterations is achieved by using explicit approach(no. of iteration =1401)

Conclusion

Therefore, we conclude that the fastest simulation in steady-state is achieved by successive over relaxation (SOR) method and fastest simulation in transient state is achieved by explicit approach.